I did a similar road trip last year that wente up through the centre of the North Island and then around the est coast on the way back. I filled my tank 7 times and I spent round $400 on gas, and thats including driving down the south island. Not too bad for a 300hp car (I wound the boost down to wastgate pressure

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I stayed at backpackers the whole time and there was plenty of parking at all of them. All up it cost me round $900 for everything, but it was a bloody good drive. Scared a couple of hitchhikers from Wellinton to Levin and Taupo to Napier. Haha.